Oscillations of a Mass-Spring System on an Inclined Plane

This Demonstration shows the oscillations of a system composed of two identical springs with force constant attached to a disk of radius and mass that rolls without sliding on a plane inclined at angle . The resultant amplitude is .
  • Contributed by: Edwin Loaiza Acuña
  • (Universidad del Valle sede Buga. Guadalajara de Buga, Colombia, Sudamérica)

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Using Newton's second law, it is possible to establish the equilibrium point , where is the length of the incline, is the acceleration due to gravity, and is a parameter that determines the rotation of the wheel. By energy conservation, one can find the angular frequency: . From this, the equation of motion for the coordinate, measured along the surface, is found to be . The parameters , , , , and all appear in the result.
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